Problem: Simplify the expression. $ (3n^{4}+6n) - ( -n^{4}+4n^{3}) - ( -n^{4}-n^{2}) $
Solution: Distribute any negative signs. $(3n^{4}+6n) + (n^{4}-4n^{3}) + (n^{4}+n^{2})$ Since we are adding polynomials, we can simply remove the parentheses. $3n^{4}+6n + n^{4}-4n^{3} + n^{4}+n^{2}$ Identify like terms. $ {3 n^4} + \color{#9D38BD}{6 n} + { n^4} - \color{#DF0030}{4 n^3} + { n^4} + { n^2} $ Combine like terms. $ { ( 3 + 1 + 1 ) n^4} + \color{#DF0030}{ -4 n^3} + { n^2} + \color{#9D38BD}{ 6 n} $ Add the coefficients. $5n^{4}-4n^{3}+n^{2}+6n$